Studying the Performance of the Jellyfish Search Optimiser for the Application of Projection Pursuit

H. Sherry Zhang

University of Texas at Austin

Sep 4, 2024

Optimisation in projection pursuit

  • Data: \(\mathbf{X}_{n \times p}\); Basis: \(\mathbf{A}_{p\times d}\)
  • Projection: \(\mathbf{Y} = \mathbf{X} \cdot \mathbf{A}\)
  • Index function: \(f: \mathbb{R}^{n \times d} \mapsto \mathbb{R}\)
  • Optimisation: \(\arg \max_{\mathbf{A}} f(\mathbf{X} \cdot \mathbf{A}) ~~~ s.t. ~~~ \mathbf{A}^{\prime} \mathbf{A} = I_d\)
  • 5 vars (\(x_1\) - \(x_5\)), 1000 obs simulated
    • One variable (\(x_2\)) is a mixture normal
    • others are random normal
  • 1D projection using the holes index: \(\propto 1 -\frac{1}{n} \sum_{i = 1}^n \exp(-\frac{1}{2} y_i y_i^{\prime})\)

Motivation

The work also reveals inadequacies in the tour optimization algorithm, that may benefit from newly developed techniques and software tools. Exploring this area would help improve the guided tours. As new optimization techniques become available, adapting these to the guided tour would extend the technique to a broader range of problems. (Laa & Cook, 2020)

Continuation of the previous work

The Jellyfish search optimiser

Chou, J. S., & Truong, D. N. (2021). A novel metaheuristic optimizer inspired by behavior of jellyfish in ocean. Applied Mathematics and Computation, 389, 125535.

Properties proposed

smoothness, squintability, flexibility, rotation invariance, speed

Smoothness

Squintability

Example:

Simulation setup

Results

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